Basic Math Examples

$\frac{1 + \frac{5}{9}}{4 \frac{2}{9}}$

Step 1

Convert $4 \frac{2}{9}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{1 + \frac{5}{9}}{4 + \frac{2}{9}}$

Step 1.2

Add $4$ and $\frac{2}{9}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{1 + \frac{5}{9}}{4 \cdot \frac{9}{9} + \frac{2}{9}}$

Step 1.2.2

Combine $4$ and $\frac{9}{9}$ .

$\frac{1 + \frac{5}{9}}{\frac{4 \cdot 9}{9} + \frac{2}{9}}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{1 + \frac{5}{9}}{\frac{4 \cdot 9 + 2}{9}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $9$ .

$\frac{1 + \frac{5}{9}}{\frac{36 + 2}{9}}$

Step 1.2.4.2

Add $36$ and $2$ .

$\frac{1 + \frac{5}{9}}{\frac{38}{9}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$(1 + \frac{5}{9}) \frac{9}{38}$

Step 3

Simplify the expression.

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Step 3.1

Write $1$ as a fraction with a common denominator.

$(\frac{9}{9} + \frac{5}{9}) \frac{9}{38}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{9 + 5}{9} \cdot \frac{9}{38}$

Step 3.3

Add $9$ and $5$ .

$\frac{14}{9} \cdot \frac{9}{38}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $14$ .

$\frac{2 (7)}{9} \cdot \frac{9}{38}$

Step 4.2

Factor $2$ out of $38$ .

$\frac{2 \cdot 7}{9} \cdot \frac{9}{2 \cdot 19}$

Step 4.3

Cancel the common factor.

$\frac{2 \cdot 7}{9} \cdot \frac{9}{2 \cdot 19}$

Step 4.4

Rewrite the expression.

$\frac{7}{9} \cdot \frac{9}{19}$

Step 5

Cancel the common factor of $9$ .

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Step 5.1

Cancel the common factor.

$\frac{7}{9} \cdot \frac{9}{19}$

Step 5.2

Rewrite the expression.

$7 (\frac{1}{19})$

Step 6

Combine $7$ and $\frac{1}{19}$ .

$\frac{7}{19}$